water

Technical Note

Wave Climate at Shallow Waters along the AbuDhabi Coast

Waleed Hamza 1, Letizia Lusito 2,* ID , Francesco Ligorio 2, Giuseppe Roberto Tomasicchio 2 andFelice D’Alessandro 2

1 Biology Department, College of Science, United Arab Emirates University, 15551 Al Ain, UAE;w.hamza@uaeu.ac.ae

2 Department of Engineering for Innovation, University of Salento, Campus Ecotekne, 73100 Lecce, Italy;francesco.ligorio@unisalento.it (F.L.); roberto.tomasicchio@unisalento.it (G.R.T.);felice.dalessandro@unisalento.it (F.D.)

* Correspondence: letizia.lusito@unisalento.it

Received: 3 July 2018; Accepted: 18 July 2018; Published: 26 July 2018�����������������

Abstract: High-resolution, reliable global atmospheric and oceanic numerical models can represent akey factor in designing a coastal intervention. At the present, two main centers have the capabilities toproduce them: the National Oceanic and Atmospheric Administration (NOAA) in the U.S.A. and theEuropean Centre for Medium-Range Weather Forecasts (ECMWF). The NOAA and ECMWF wavemodels are developed, in particular, for different water regions: deep, intermediate, and shallowwater regions using different types of spatial and temporal grids. Recently, in the Arabian Gulf (alsonamed Persian Gulf), the Abu Dhabi Municipality (ADM) installed an ADCP (Acoustic DopplerCurrent Profiler) to observe the atmospheric and oceanographic conditions (water level, significantwave height, peak wave period, water temperature, and wind speed and direction) at 6 m waterdepth, in the vicinity of the shoreline of the Saadiyat beach. Courtesy of Abu Dhabi Municipality,this observations dataset is available; the recorded data span the period from June 2015 to January2018 (included), with a time resolution of 10 min and 30 min for the atmospheric and oceanographicvariables, respectively. At the ADCP deployment location (ADMins), the wave climate has beendetermined using wave propagation of the NOAA offshore wave dataset by means of the SimulatingWAves Nearshore (SWAN) numerical model, the NOAA and ECMWF wave datasets at the closestgrid point in shallow water conditions, and the SPM ’84 hindcasting method with the NOAA winddataset used as input. It is shown that the best agreement with the observed wave climate is obtainedusing the SPM ’84 hindcasting method for the shallow water conditions.

Keywords: wave hindcasting; Abu Dhabi; shallow waters; Shore Protection Manual; wave climate

1. Introduction

The United Arab Emirates (UAE) is an Arabian Gulf (also named Persian Gulf) nation with anextended coastal area, comprising more than 700 km of coastline and embracing many different shallowwater wetland habitats. Some areas of the Abu Dhabi coastline are undergoing a large developmentwith residential, business, cultural, and tourism infrastructure (http://government.ae/en/about-the-uae/uae-future). As a consequence, there is an increasing need for a detailed knowledge of the waveconditions in order to design the coastal interventions [1–4].

The present study focuses on Saadiyat (Figure 1), a large low-lying 27 km2 island situated inthe Gulf within the Emirate of Abu Dhabi. Saadiyat island hosts a vast national park of mangrovesand a 9 km SW–NE oriented natural sandy beach, Saadiyat beach, populated by numerous flora andfauna species. Part of the island is undergoing a considerable development program. In March 2015,

Water 2018, 10, 985; doi:10.3390/w10080985 www.mdpi.com/journal/water

Water 2018, 10, 985 2 of 19

the “North Beach Phase 1 Development Plans” document was submitted to the Abu Dhabi UrbanPlanning Council as a part of the Shoreline Protection Works Master Plan, an addendum to the ConceptMaster Plan of the Saadiyat Cultural District. The urban plan includes the construction of new luxuryhotels, a private luxury residential area, and the Cultural District with the Louvre and Guggenheimmuseums (Figure 2).

Water 2018, 10, x FOR PEER REVIEW 2 of 19

species. Part of the island is undergoing a considerable development program. In March 2015, the “North Beach Phase 1 Development Plans” document was submitted to the Abu Dhabi Urban Planning Council as a part of the Shoreline Protection Works Master Plan, an addendum to the Concept Master Plan of the Saadiyat Cultural District. The urban plan includes the construction of new luxury hotels, a private luxury residential area, and the Cultural District with the Louvre and Guggenheim museums (Figure 2).

Figure 1. Aerial view of Saadiyat beach.

Figure 2. Concept Master Plan of Saadiyat Cultural District (courtesy Tourism Development & Investment Company).

Figure 1. Aerial view of Saadiyat beach.

Water 2018, 10, x FOR PEER REVIEW 2 of 19

species. Part of the island is undergoing a considerable development program. In March 2015, the “North Beach Phase 1 Development Plans” document was submitted to the Abu Dhabi Urban Planning Council as a part of the Shoreline Protection Works Master Plan, an addendum to the Concept Master Plan of the Saadiyat Cultural District. The urban plan includes the construction of new luxury hotels, a private luxury residential area, and the Cultural District with the Louvre and Guggenheim museums (Figure 2).

Figure 1. Aerial view of Saadiyat beach.

Figure 2. Concept Master Plan of Saadiyat Cultural District (courtesy Tourism Development & Investment Company).

Figure 2. Concept Master Plan of Saadiyat Cultural District (courtesy Tourism Development &Investment Company).

Water 2018, 10, 985 3 of 19

At present, professionals involved in the Abu Dhabi coastal development typically use two mainsources of wind and wave data: the National Oceanic and Atmospheric Administration (NOAA) andthe European Centre for Medium-Range Weather Forecasts (ECMWF), following the well consolidatedscientific methods already developed for the analysis of shallow water coastal areas [5–9].

To overcome the scarcity of in situ observations in the area, the Abu Dhabi Municipality (ADM)has recently installed several instruments in the vicinity of the Abu Dhabi coastline at different waterdepths. Within a research project granted by the National Water Center at the United Arab EmiratesUniversity, the new in situ observed wave conditions dataset has been made available.

The in situ observed wave dataset allows for the comparison and verification of data fromother sources, such as the NOAA and ECMWF global wave models, third-generation shallow watermodels such as the Simulating WAves Nearshore (SWAN) [10,11], and second-generation local wavemodels [12]. The comparison and verification method used is the Shore Protection Manual ’84 (SPM’84) method [1], a second-generation wave hindcasting method widely used for local hindcasting.SPM ’84 has been selected because of its simplicity in the algorithms and because it allowed for theconsideration of different wave regions. SWAN has been already successfully used to model waves incoastal regions [13–19].

The SPM ’84 method allows the estimation of the wave characteristics using wind data (intensity,direction and duration of the event) at a reference height of 10 m above sea water level, and theeffective fetch value. It has been used to calculate the wave conditions at the location where the ADMinstrument (ADMins) is deployed from the NOAA wind data, which are provided at 10 m above seawater level.

The comparison and verification of data from NOAA, ECMWF, and SPM ’84 has been conductedunder the assumption that the ADMins and the closest NOAA and ECMWF nodes are exposed tohomogeneous atmospheric and oceanographic conditions [20,21].

The present paper is organized as follows: Section 2 presents a review of the state-of-the-art ofatmospheric and oceanographic global numerical models and the description of the application of theSPM ’84 parametric local wave growth method, Section 3 describes the results, and Section 4 discussesthe results from the use of the SPM ’84 wave hindcasting and the adopted verification procedure.

2. Materials and Methods

Recently, the ADM installed an instrument to observe atmospheric (wind speed and direction)and oceanographic (water level, significant wave height, peak wave period, water temperature)characteristics close to the shoreline of the Saadiyat beach. The instrument, an Argonaut-XR producedby the company “SonTek—A Xylem Brand” (San Diego, CA, USA), is a 3-D up-looking monostaticAcoustic Doppler Current Profiler (ADCP) that uses sonar for precise water velocity measurements.Monostatic refers to the fact that the same transducer is used as a transmitter and receiver, with asampling frequency of 1.5 MHz. Recorded data from June 2015 to January 2018 (included) wereavailable at a time resolution of 10 and 30 min for the atmospheric and oceanographic variables,respectively. The deployed Argonaut-XR presented a limitation: the profiler had not been equippedwith the software/hardware necessary to also measure wave spectra; therefore, the instrument couldnot measure the wave directions directly.

Direct wave measurements are considered the most reliable source of information. In the Gulf area,this type of information is rare or even missing. The Abu Dhabi Municipality started to monitor thewave conditions only four years ago. Other Municipalities in the UAE do not provide directly observeddata. As a consequence, at present, the only reliable source of wave data in Abu Dhabi is to considerthe new in situ observed wave conditions dataset of sufficient length to represent a mean annual waveclimate in relation to the weather conditions in the area, which are quite mild, characterized by theabsence of extreme wind conditions (e.g., hurricanes) and extreme wave conditions, due to the factthat the Gulf is an enclosed basin. The wave observations, recorded by the ADCP, have been compared

Water 2018, 10, 985 4 of 19

to wave numerical models, designed by some of the major oceanography research centers all overthe world.

The first considered model is designed by NOAA. The NOAA National Centers for EnvironmentalPrediction (NCEP) developed the Climate Forecast System (CFS), a fully coupled model representingthe interaction between the Earth’s atmosphere, oceans, land, and sea ice. A reanalysis of thesea and atmosphere state for the period of 1979–2009 has been conducted, resulting in the CFSReanalysis (CFSR) dataset [22]. The purpose of the CFSR is to produce multiyear global, state-of-the-artgridded representations of atmospheric and oceanic states, generated by a consistent model and dataassimilation system. The vertical discretization of the atmosphere consists of 64 layers. The temporalresolution for the atmospheric variables is 3 h. Using the CFSR dataset, the NOAA Marine Modelingand Analysis Branch (MMAB) has produced a wave hindcast for the same period. The wave hindcastdataset has been generated using the WAVEWATCH III (WW3) model (v3.14), and it is suitable for usein climate studies. The wave model suite consists of global and regional nested grids. The rectilineargrids were developed using ETOPO-1 bathymetry [23], together with v1.10 of the Global Self-consistentHierarchical High-resolution Shoreline (GSHHS) database. The higher-resolution North West IndianOcean bathymetry grid, adopted in the considered data, has a resolution of 10 arc-minutes (1/6◦).The WW3 model is run using a 30 arc-minute computational resolution, but the results are interpolatedon a 10 arc-minute numerical grid. The spatial resolution of the considered data is, therefore, 1/6◦,which corresponds to roughly 20 km. The North West Indian Ocean computational grid, adopted inthe considered data, extends in longitude from 30◦ E to 70◦ E (with 241 grid nodes) and in latitude from20◦ S to 31◦ N (307 grid nodes). As wave characteristics are dominated by wind dynamics, it is possibleto achieve an accurate wave hindcast by using statistically homogeneous wind fields from a long-termreanalysis such as the CFSR, without the need for wave data assimilation [24–26]. The NOAA datasets(both wind and waves) are freely available. The NOAA WAVEWATCH III/CFSR webpages [27,28]present additional details about the datasets.

The second of the considered wave hindcasting methods is designed by the European Centrefor Medium-Range Weather Forecasts (ECMWF) and it is named ERA-Interim. The ERA-interimdataset is another global atmospheric reanalysis, starting from 1979 and is continuously updated. It isbased on the Cy31r2 version of the Integrated Forecasting System (IFS). It also models oceanographicvariables, including waves. The atmospheric configuration uses 60 vertical model levels and a 6-hourlytemporal resolution [29,30]. The wave model is based on WAM [31,32], resolving 30 wave frequenciesand 24 wave directions. The wave model contains corrections for treating unresolved bathymetryeffects and a reformulation of the dissipation source term. The bathymetric information is based onthe ETOPO-2 bathymetry, with a 2 arc-minute resolution (1/30◦). The computational grid resolutionfor the wave model is 80 km [33], but the output grid has been interpolated onto a finer mesh, of 1/8◦

horizontal resolution. The ECMWF ERA-Interim dataset is available upon request on the ECMWFservers. Further information on how to access the data can be found at Reference [34].

The SPM ’84 method [1] is a parametric wave hindcasting method; it allows for the determinationof the significant wave height (Hs) and peak period (Tp) from (i) the geographical extent of the areawhere the constant wind is blowing, indicated as fetch (F), (ii) the wind duration (t), and (iii) the depthof water in the generation area (d) [35]. Fetches are related to the curvature of the isobars describingthe weather system at the origin of the wave growth. The extent of a typical weather system results inan upper limit for fetches of roughly 500 km.

Given the relative values of F, Tp, and t, the sea state is classified as follows:

• Fully Arisen Sea (FAS), where any added wind energy is balanced by wave energy dissipationand the waves have the maximum possible height;

• Fetch-Limited Sea (FL), where the wave height is limited by the length of the fetch over which thewind has blown; or

• Duration-Limited Sea (DL), where the wave height is limited by the duration of thewind conditions.

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The SPM ’84 method determines the spectral significant wave height Hm0 from σ, the variance ofthe sea surface elevation, according to:

Hm0 = 4σ = 4√

m0 (1)

where m0 is the zero moment of the wave spectrum, i.e., the area under the spectrum itself. In deepwater, Hm0 is approximately equal to Hs; in shallow water, Hm0 becomes less than Hs.

The wave growth formulas at both deep and shallow waters are given in terms of the wind stressfactor UA (adjusted windspeed or wind stress), which is related to the normal windspeed at a heightof 10 m, U, by the following equation:

UA = 0.71 U1.23 (2)

where both UA and U are measured in m/s. The SPM ’84 method is based on the assumption thatthe wave growth is entirely caused by a wind blowing at a constant speed and direction for a givenduration over the specific fetch area. The wind direction is considered constant if it varies from thewind direction mean by less than 15◦, and the wind speed is considered constant if it varies from thewind speed mean by less than 2.5 m/s. With these assumptions and considerations, the equationsfor wave growth hindcasting/forecasting at shallow water conditions for fully arisen, fetch-limited,and duration-limited sea conditions have been determined. These equations are derived from theanalogous deep-water equations [1] with the additional condition that the wave energy is furtherreduced due to additional effects like bottom friction.

In the present application of wave hindcasting in the Arabian Gulf area, the SPM ’84 input dataare the ADMins effective fetches, F [36,37]; the water depth at the ADMins, d (equal to 6 m); the windstress and direction of the wind generating the waves in proximity of ADMins, taken from the NOAACFSR grid point which is the closest to the ADMins; and the wind duration, t. In the case of Saadiyatbeach, there are two NOAA CFSR grid points that are similarly distant from ADMins (Figure 3), locatedat the north and at the south of the ADMins; in the following, these two grid points will be indicatedas NOAA North (NOAA N) and NOAA South (NOAA S). Figure 3 shows the location of the ADMins,the NOAA N and NOAA S grid nodes and the location of the ECMWF grid point. Table 1 reports thecoordinates of these grid points, with their corresponding water depths.

Table 1. ADMins, NOAA N, NOAA S, ECMWF, NOAA Offshore coordinates, and water depths.

Name Longitude (◦E) Latitude (◦N) Water Depth (m)

ADMins 54◦24′29” 24◦34′17” 6NOAA North 54◦30′00” 24◦40′00” 6NOAA South 54◦19′59” 24◦30′00” 3

ECMWF 54◦22′30” 24◦37′30” 11NOAA Offshore 54◦00′00” 25◦00′00” 21

Figure 4 shows the NOAA N (a) and NOAA S (b) wind rose, indicating that the atmosphericconditions at the two locations can be considered uniform. In fact, the NOAA N and NOAA S nodesare exposed to the same atmospheric conditions, given the relatively small distance between the twonodes. Because of this similarity, for the SPM ’84 application, only the data from the north node havebeen considered; in particular, the wind stress UA,N , and wind direction, θ.

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Figure 3. Bathymetry of the Saadiyat area, where markers show the position of ADMins, the NOAA N, the NOAA S, the NOAA offshore and the ECMWF model nodes.

(a) (b)

Figure 4. NOAA wind rose at the north node (a), and at the south node (b), in proximity of the ADMins, indicating that the atmospheric conditions along this stretch of coast can be considered uniform.

Figure 3. Bathymetry of the Saadiyat area, where markers show the position of ADMins, the NOAA N,the NOAA S, the NOAA offshore and the ECMWF model nodes.

E

N-E

N

N-W

W

S-W

S

S-E

5%10%

Wind speed [m/s][1.00 - 2.00][2.00 - 3.00][3.00 - 4.00]

[4.00 - 5.00][5.00 - 6.00][6.00 - 7.00]

[7.00 - 8.00][8.00 - 10.00]> 10.00

E

N-E

N

N-W

W

S-W

S

S-E

5%10%

Wind speed [m/s][1.00 - 2.00][2.00 - 3.00][3.00 - 4.00]

[4.00 - 5.00][5.00 - 6.00][6.00 - 7.00]

[7.00 - 8.00][8.00 - 10.00]> 10.00

(a) (b)

Figure 4. NOAA wind rose at the north node (a), and at the south node (b), in proximity of the ADMins,indicating that the atmospheric conditions along this stretch of coast can be considered uniform.

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The NOAA N wind time series, consisting of approximately 90,000 points, was used to determinean averaged time series of steady wind in both magnitude and direction. A wind measurement datum,i, was considered to belong to a steady weather phenomenon if the following is true:

• |Ui − < Uj>| ≤ 2.5 m/s

• |θi − <θj >| ≤ 15◦

where the symbol <Uj> indicated the average of the wind speed calculated over the j points before theith, already previously “clustered” in a steady wind condition. The same procedure applied for <θj>.If the ith point met the steady state condition, a new average was calculated, aggregating the ith pointto the other j. The cluster then contained j + 1 points. Then, the successive point was examined. If apoint did not satisfy these conditions, the time-cluster was closed and the location was consideredto be subject to a new different wind condition afterwards [38]. The procedure described above isindicated in the following as a “dynamical running average” (DRA). Figure 5 shows the result of theDRA procedure for August 2009. The top panel shows the time series of the wind speed (red) and thedynamically averaged wind speed (blue). The bottom figure shows time series of the wind direction(red) and the dynamically averaged wind direction (blue).Water 2018, 10, x FOR PEER REVIEW 7 of 19

Figure 5. Top panel: time series of the wind speed (red) and the dynamical running averaged wind speed (blue). Bottom panel: time series of the wind direction (red) and the dynamically averaged wind direction (blue).

Table 1. ADMins, NOAA N, NOAA S, ECMWF, NOAA Offshore coordinates, and water depths.

Name Longitude (°E) Latitude (°N) Water Depth (m) ADMins 54°24′29′′ 24°34′17′′ 6

NOAA North 54°30′00′′ 24°40′00′′ 6 NOAA South 54°19′59′′ 24°30′00′′ 3

ECMWF 54°22′30′′ 24°37′30′′ 11 NOAA Offshore 54°00′00′′ 25°00′00′′ 21

Comparing the DRA wind speed and direction time series (Figure 5, blue lines), only segments where DRA time series are flat in both the wind speed and direction time series were considered (Figure 5, green vertical line). These segments indicated periods of time where the wind conditions were steady (constant). Therefore, the time period between the beginning and the end of these segments has been assumed as the wind duration tADMins of the steady wind phenomenon generating the waves (Figure 6, orange horizontal line). In the example in Figure 6, the resulting duration of the particular wind phenomenon was 15 h (5 data points with 3 h time resolution). If no flat segment could be identified in both the DRA time series, the wind duration was assumed to be 3 h (equal to the time resolution of the original time series).

Having determined the duration of the wind generating the waves, it was possible to apply the SPM ’84 method at the ADMins location, as explained in the following. The wave direction at the ADMins θwave,ADMins was calculated considering the wind–wave direction correlation [39]. Sea regimes (FAS, FL, DL) at the ADMins location, where the water depth was 6 m, were determined as in Reference [40]. If the factor: ,( ∙ ) 0.83 (3)

FAS exists at the ADMins.

Figure 5. Top panel: time series of the wind speed (red) and the dynamical running averaged windspeed (blue). Bottom panel: time series of the wind direction (red) and the dynamically averaged winddirection (blue).

Comparing the DRA wind speed and direction time series (Figure 5, blue lines), only segmentswhere DRA time series are flat in both the wind speed and direction time series were considered(Figure 5, green vertical line). These segments indicated periods of time where the wind conditionswere steady (constant). Therefore, the time period between the beginning and the end of thesesegments has been assumed as the wind duration tADMins of the steady wind phenomenon generatingthe waves (Figure 6, orange horizontal line). In the example in Figure 6, the resulting duration of theparticular wind phenomenon was 15 h (5 data points with 3 h time resolution). If no flat segmentcould be identified in both the DRA time series, the wind duration was assumed to be 3 h (equal to thetime resolution of the original time series).

Having determined the duration of the wind generating the waves, it was possible to applythe SPM ’84 method at the ADMins location, as explained in the following. The wave direction

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at the ADMins θwave,ADMins was calculated considering the wind–wave direction correlation [39].Sea regimes (FAS, FL, DL) at the ADMins location, where the water depth d was 6 m, were determinedas in Reference [40]. If the factor:

UA,N

(g · d)12< 0.83 (3)

FAS exists at the ADMins.Water 2018, 10, x FOR PEER REVIEW 8 of 19

Figure 6. Determination of the duration of the steady wind generating the waves (zoom of Figure 5).

If the ADMins is under the FAS condition, the significant wave height, , , was calculated as:

, = , 0.283 0.530 ∙, (4)

where all the SI units are adopted. If the ADMins was not under the FAS condition, the duration tADMins was compared to the minimum duration, tmin, necessary for establishing the FL condition. The minimum duration was calculated as in Reference [38]:

= 2.59 ∙ , ∙ ∙, (5)

where is an average water depth along the fetch extension. In this case, = 30 . If tADMins < tmin, the location was in the DL condition, otherwise it was in the FL condition.

In the FL condition, the significant wave height at the ADMins, , , was calculated as:

, = , 0.283 0.530 ∙, ∙ 0.00565 ∙ ∙ , ,⁄tanh 0.530 ∙,

(6)

In the DL condition, from Equation (5), a new effective fetch ′ , was calculated by considering tmin = tADMins and used in Equation (6) to calculate , in DL conditions.

Another approach to calculate the wave climate at the ADMins location consisted of propagating the wave dataset at the offshore NOAA grid point towards the coastline. Wave propagation from offshore to ADMins was performed by means of the numerical model SWAN [10,11], which is a third generation fully-spectral wind-wave model developed at the Delft University of Technology (The Netherlands) that simulates random, short-crested wind generated waves in coastal regions.

The offshore wave time series was extracted from the NOAA CFSR model at coordinates 54°00′00′′ E, 25°00′00′′ N, with water depth equal to 21 m (Figure 3 and Table 1). SWAN was run in stationary mode, in which waves are assumed to propagate instantaneously throughout the model domain. This assumption was reasonable for the small domain and slowly varying forcing conditions for this case. Nonlinear triad interactions [41,42] were significantly larger than quartet interactions for the short spatial scales and shallow depths considered here, and thus quartet interactions were neglected. The model runs included the Madsen expression for bottom friction

Figure 6. Determination of the duration of the steady wind generating the waves (zoom of Figure 5).

If the ADMins is under the FAS condition, the significant wave height, Hs,ADMins, wascalculated as:

Hs,ADMins =U2

A,N

g0.283 tanh

0.530

(g · d

U2A,N

) 34 (4)

where all the SI units are adopted. If the ADMins was not under the FAS condition, the durationtADMins was compared to the minimum duration, tmin, necessary for establishing the FL condition.The minimum duration was calculated as in Reference [38]:

tmin = 2.59 ·Fe f f ,ADMins

d̂·(

g · d̂U2

A,N

) 23

(5)

where d̂ is an average water depth along the fetch extension. In this case, d̂ = 30 m. If tADMins < tmin,the location was in the DL condition, otherwise it was in the FL condition.

In the FL condition, the significant wave height at the ADMins, Hs,ADMins, was calculated as:

Hs,ADMins =U2

A,N

g0.283 tanh

0.530

(g · d

U2A,N

) 34 · tanh

0.00565 ·

(g · Fe f f ,T/U2

A,N

) 12

tan h

[0.530

(g·d

U2A,N

) 34]

(6)

In the DL condition, from Equation (5), a new effective fetch F′e f f ,ADMins was calculated byconsidering tmin = tADMins and used in Equation (6) to calculate Hs,ADMins in DL conditions.

Another approach to calculate the wave climate at the ADMins location consisted of propagatingthe wave dataset at the offshore NOAA grid point towards the coastline. Wave propagation fromoffshore to ADMins was performed by means of the numerical model SWAN [10,11], which is a

Water 2018, 10, 985 9 of 19

third generation fully-spectral wind-wave model developed at the Delft University of Technology(The Netherlands) that simulates random, short-crested wind generated waves in coastal regions.

The offshore wave time series was extracted from the NOAA CFSR model at coordinates54◦00′00” E, 25◦00′00” N, with water depth equal to 21 m (Figure 3 and Table 1). SWAN was run instationary mode, in which waves are assumed to propagate instantaneously throughout the modeldomain. This assumption was reasonable for the small domain and slowly varying forcing conditionsfor this case. Nonlinear triad interactions [41,42] were significantly larger than quartet interactionsfor the short spatial scales and shallow depths considered here, and thus quartet interactions wereneglected. The model runs included the Madsen expression for bottom friction dissipation [43] using acoefficient of 0.001 m. Breaking wave dissipation was estimated with a bore-based model [44], with thedepth-induced constant wave breaking parameter γ = 0.73, found as the mean value of the datasetof Battjes and Stive [45,46]. The frequency, f, and the directional resolution, δ, were defined using theSWAN default values, resulting in 24 logarithmically distributed frequency bins (e.g., ∆f ≈ 0.14f [47]over 0.04 ≤ f ≤ 1.00 Hz and 36 10◦-wide directional bins ∆δ evenly spaced over 0◦ ≤ δ < 360◦ [47]).Table 2 summarizes the main SWAN configuration parameters.

The boundary conditions on open boundaries in the north and north-north-west of thecomputational domain (Figure 3, yellow and blue lines) have been taken from the NOAA WW3re-analyses, at the coordinates 54◦00′00” E, 25◦00′00” N (Figure 3, yellow dot). Past similar works,e.g., Gorrel et al. [13], suggest that negligible errors in the computing area grids result from theassumption of uniform waves on the N and NNW cross-shore open water boundaries of the grid.The bathymetry information, provided through the “General Bathymetric Chart of the Ocean”(GEBCO) consortium, consists of a gridded terrain model for ocean and land with a spatial resolutionof 30 arc-seconds. It was generated by combining quality-controlled ship depth soundings withinterpolation between sounding points guided by satellite-derived gravity data [48,49]. Figure 3 showsalso the GEBCO bathymetry of the considered area.

Table 2. Main SWAN configuration parameters.

Model Version SWAN 41.20

Time and Spatial mode Stationary 2-dimensional

Bathymetry GEBCO_2014 (30 arc-second)

Computational domain LON: 54.00417◦ E, 54.59584◦ E

LAT: 24.00417◦ N to 25.00417◦ E

71 × 120 computational nodes

Wave frequency grid 0.04 to 1.00 Hz, 24 frequencies

Directional grid 0◦ to 360◦, 36 directions

Physics

Breaking constant breaker index, γ = 0.73

Whitecapping Komen et al., 1984 [50]

Bottom Friction Madsen et al., 1988 [43]

equiv. roughness length scale of the bottom 0.001 m

Triads included

Diffraction excluded

Quadruplets excluded

Boundary conditions N boundary: from 54.00417◦ E to 54.59584◦ E

provided by NOAA WW3 NNW boundary: from 24.834◦ N to 25.00417◦ N

Boundary wave spectra shape Jonswap [51]

Table 3 summarizes the information about the bathymetry and the computational resolution usedin SWAN, and in the NOAA and ECMWF wave models.

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Table 3. Bathymetry and the computational resolution.

Name Bathymetry Computational Grid Output Grid

Name Resolution Resolution Resolution

NOAA ETOPO-1(1 arc-minute resolution)

10 arc-minutes = 1/6◦

(interpolated)10 arc-minutes = 1/6◦

(interpolated from 1/2◦)10 arc-minutes = 1/6◦

(interpolated from 1/2◦)

ECMWF ETOPO-2(2 arc-minute resolution) 2 arc-minutes = 1/30◦ 80 km 1/8◦ (interpolated

from T255)

SWAN GEBCO 30 arc-seconds = 1/120◦ 30 arc-seconds = 1/120◦ 30 arc-seconds = 1/120◦

3. Results

Field measurements showed that the Argonaut-XR appeared to be unable to measure wave peakperiods smaller than 3 s, although the instrumental sensitivity range is 2–20 s, according to the systemmanual technical specifications [52]. Figure 7 shows the wave period normalized probability densityfunction distribution (normalised p.d.f.) as measured by the ADMins, as determined by the NOAA andthe ECMWF wave models at the closest location to the ADMins position, and as estimated by the SPM’84. Figure 7 shows a cut-off at 3 s in the peak period distribution measured by the ADMins. This is notin agreement with the results from the NOAA and ECMWF wave numerical models indicating thatwaves with a 3 s peak period appear in the area.

Water 2018, 10, x FOR PEER REVIEW 10 of 19

3. Results

Field measurements showed that the Argonaut-XR appeared to be unable to measure wave peak periods smaller than 3 s, although the instrumental sensitivity range is 2–20 s, according to the system manual technical specifications [52]. Figure 7 shows the wave period normalized probability density function distribution (normalised p.d.f.) as measured by the ADMins, as determined by the NOAA and the ECMWF wave models at the closest location to the ADMins position, and as estimated by the SPM ’84. Figure 7 shows a cut-off at 3 s in the peak period distribution measured by the ADMins. This is not in agreement with the results from the NOAA and ECMWF wave numerical models indicating that waves with a 3 s peak period appear in the area.

Figure 7. Wave period distribution (normalized p.d.f.) by ADMins, by NOAA and ECMWF datasets and by SPM ’84.

Figure 8 shows the wave roses from SPM ’84 (1979–2009) and ADMins (June 2015–January 2018). The maximum value of the significant wave height, Hs, recorded at a 6 m water depth in front of Saadiyat beach, was around 2 m. The SPM ’84 underestimates the low (0.25–0.50 m) and high (1–2 m) waves, respectively. For each wave height class, Figure 9 depicts the difference between values of appearance frequency (af) in %, determined by SPM ’84 and observed by ADMins; the difference appears to be small, therefore the af determined by SPM ’84 and observed by ADMins are in fairly good agreement. The largest differences were found for values of wave height between 1 and 1.5 m.

Figure 7. Wave period distribution (normalized p.d.f.) by ADMins, by NOAA and ECMWF datasetsand by SPM ’84.

Figure 8 shows the wave roses from SPM ’84 (1979–2009) and ADMins (June 2015–January 2018).The maximum value of the significant wave height, Hs, recorded at a 6 m water depth in front ofSaadiyat beach, was around 2 m. The SPM ’84 underestimates the low (0.25–0.50 m) and high (1–2 m)waves, respectively. For each wave height class, Figure 9 depicts the difference between values ofappearance frequency (af ) in %, determined by SPM ’84 and observed by ADMins; the differenceappears to be small, therefore the af determined by SPM ’84 and observed by ADMins are in fairlygood agreement. The largest differences were found for values of wave height between 1 and 1.5 m.

Water 2018, 10, 985 11 of 19

E

N-E

N

N-W

W

S-W

S

S-E

2.5% 5% 7.5% 10%

Wave height [m]< 0.25[0.25 - 0.50][0.50 - 1.00]

[1.00 - 1.50][1.50 - 2.00]

[2.00 - 2.50]> 2.50

E

N-E

N

N-W

W

S-W

S

S-E

2% 4% 6% 8%

Wave height [m]< 0.25[0.25 - 0.50][0.50 - 1.00]

[1.00 - 1.50][1.50 - 2.00]

[2.00 - 2.50]> 2.50

(a) (b)

Figure 8. Wave roses from SPM ’84 (a) and from ADMins (b).

Water 2018, 10, x FOR PEER REVIEW 11 of 19

(a) (b)

Figure 8. Wave roses from SPM ’84 (a) and from ADMins (b).

Figure 9. Difference in values of appearance frequency determined by SPM ’84 and observed by ADMins.

Figure 10 shows the wave roses from the NOAA and ECMWF wave models at the nodes, which were closest to ADMins. Comparing the wave roses obtained from the NOAA and ECMWF nodes at shallow water conditions (Figure 10), with the wave roses estimated by SPM ’84 and observed by ADMins (Figure 8) shows that the NOAA and ECMWF models did not sufficiently capture the variability of the wave climate at the ADMins location in shallow water conditions; in particular, for the directional distribution. The higher horizontal resolution (1/8°) of the ERA-Interim wind and waves hindcasted datasets allowed ECMWF to model the waves having Hs between 1.5 and 2 m with better precision compared to NOAA.

Figure 9. Difference in values of appearance frequency determined by SPM ’84 and observedby ADMins.

Figure 10 shows the wave roses from the NOAA and ECMWF wave models at the nodes, whichwere closest to ADMins. Comparing the wave roses obtained from the NOAA and ECMWF nodesat shallow water conditions (Figure 10), with the wave roses estimated by SPM ’84 and observedby ADMins (Figure 8) shows that the NOAA and ECMWF models did not sufficiently capture thevariability of the wave climate at the ADMins location in shallow water conditions; in particular, for thedirectional distribution. The higher horizontal resolution (1/8◦) of the ERA-Interim wind and waveshindcasted datasets allowed ECMWF to model the waves having Hs between 1.5 and 2 m with betterprecision compared to NOAA.

Water 2018, 10, 985 12 of 19

E

N-E

N

N-W

W

S-W

S

S-E

10% 20% 30% 40%

Wave height [m]< 0.25[0.25 - 0.50][0.50 - 1.00]

[1.00 - 1.50][1.50 - 2.00]

[2.00 - 2.50]> 2.50

E

N-E

N

N-W

W

S-W

S

S-E

10%20%

30%

Wave height [m]< 0.25[0.25 - 0.50][0.50 - 1.00]

[1.00 - 1.50][1.50 - 2.00]

[2.00 - 2.50]> 2.50

E

N-E

N

N-W

W

S-W

S

S-E

10% 20% 30% 40%

Wave height [m]< 0.25[0.25 - 0.50][0.50 - 1.00]

[1.00 - 1.50][1.50 - 2.00]

[2.00 - 2.50]> 2.50

(a) (b) (c)

Figure 10. NOAA wave rose at the north node (a), NOAA wave rose at the south node (b), and ECMWF(c) wave rose in proximity of the ADMins.

Figure 11 shows the SWAN-computed wave rose at the ADMins location. As for the ADMinsand SPM ’84, also in this case, the majority of the waves at Saadiyat beach came from the north-westdirection, having a wave height of up to 2 m.

Water 2018, 10, x FOR PEER REVIEW 12 of 19

(a) (b) (c)

Figure 10. NOAA wave rose at the north node (a), NOAA wave rose at the south node (b), and ECMWF (c) wave rose in proximity of the ADMins.

Figure 11 shows the SWAN-computed wave rose at the ADMins location. As for the ADMins and SPM ’84, also in this case, the majority of the waves at Saadiyat beach came from the north-west direction, having a wave height of up to 2 m.

Comparing the results from SWAN and SPM ’84 with the observations at the ADMins location, it followed that SWAN was able to reproduce waves with low and high Hs better than the SPM ’84, but the SPM ’84 wave directional distribution presented a better agreement with the observations.

Figure 11. SWAN-computed wave rose at the ADMins location.

To summarize, Table 4 shows the observed/modelled appearance frequency (af) (in %) in the main sector (NW or numerically 315 ± 22.5°), divided in seven classes of Hs.

Figure 11. SWAN-computed wave rose at the ADMins location.

Comparing the results from SWAN and SPM ’84 with the observations at the ADMins location,it followed that SWAN was able to reproduce waves with low and high Hs better than the SPM ’84,but the SPM ’84 wave directional distribution presented a better agreement with the observations.

To summarize, Table 4 shows the observed/modelled appearance frequency (af ) (in %) in themain sector (NW or numerically 315 ± 22.5◦), divided in seven classes of Hs.

Water 2018, 10, 985 13 of 19

Table 4. NW af, for classes of Hs.

DatasetClasses of HS (m)

[0, 0.25] [0.25, 0.5] [0.5, 1.0] [1.0, 1.5] [1.5, 2.0] [2.0, 2.5] >2.5

ADMins(O) 7.23 5.59 7.01 3.53 0.38 0.05 0.01

SWAN 14.88 22.25 19.33 6.68 3.48 0.70 0.00SPM ’84 4.48 7.26 15.45 0.97 0.00 0.00 0.00

NOAA N 7.90 38.99 17.63 1.68 0.03 0.00 0.00NOAA S 4.76 39.01 16.47 0.86 0.00 0.00 0.00ECMWF 12.66 25.29 20.16 7.49 2.85 0.59 0.10

With reference to the observations at the ADMins (O), Table 5 shows the af BIAS, af Root MeanSquare Error (RMSE), af Normalized BIAS (NBIAS), af Normalized RMSE (NRMSE), Symmetric MeanAbsolute Percentage Error (SMAPE), and symmetric RMSE (SRMSE) for the modelled values (M)by: SPM’ 84, SWAN, NOAA N, NOAA S, and ECMWF with respect to the observations, calculatedaccording to:

BIAS =∑7

i=1(Mi −Oi)

N(7)

RMSE =

√∑7

i=1(Mi −Oi)2

N(8)

NBIAS =∑7

i=1[(Mi −Oi)/Oi]

N(9)

NRMSE =

√∑7

i=1[(Mi −Oi)/Oi]2

N(10)

SMAPE =1N

7

∑1=1

∣∣∣∣∣Mi −Oi(Mi+Oi)

2

∣∣∣∣∣ (11)

SRMSE =

√√√√√√∑7i=1

{Mi−Oi[(Mi+Oi)

2

]}2

N(12)

where the index i indicates the Hs class (i = 1, 2, . . . , 7) and N = 7, the number of classes of Hs.SPM ’84 presented the lowest af RMSE (3.55%), indicating that the standard deviation of the af

residuals, i.e., the model error was equal to 3.55% for events in the NW sector. The SWAN af RMSE(8.52%) was lower compared to NOAA N (13.27%) and S (13.20%), and ECMWF (9.36%), confirmingthe good performance of SWAN under shallow water conditions with respect to the global scale wavemodels, WAM/WW3, which are more suitable for oceanic large-scale applications.

The main drawbacks of the use of RMSE solely in calculating model performance are the scaledependency (if the model includes variables with different scales or magnitudes, then absolute errormeasures could not be applied), the high influence of outliers in data on the model performanceevaluation, and the low reliability (the results could be different depending on the different fractionof data) [53]. For these reasons, Table 5 shows not only absolute model error statistical indicators,such as BIAS and RMSE, but also indicators based on percentage errors, such as NBIAS and NRMSE.The advantage of such indicators is that they do not depend on the scale of the observations.The disadvantages are that (i) they include a division by 0 if observed data values are very small,(ii) the very high weight of outliers in the final result, (iii) the “asymmetry issue”, and (iv) the errorvalues differ whether the predicted value is bigger or smaller than the actual. For these reasons, a third

Water 2018, 10, 985 14 of 19

group of statistical indicators is considered: the so-called “symmetric error” indicators, which are theSMAPE and the SRMSE.

Table 5. Wave model errors’ statistical indicators.

Dataset af BIAS af RMSE af NBIAS af NRMSE af SMAPE af SRMSE

SWAN 6.22 8.52 3.84 5.98 1.25 1.35SPM ’84 0.62 3.55 -0.37 0.86 1.23 1.42

NOAA N 6.06 13.27 0.59 2.42 1.27 1.44NOAA S 5.33 13.20 0.46 2.43 1.42 1.54ECMWF 6.48 9.36 4.80 6.07 1.19 1.27

Table 5 shows that the performance of SPM ’84 was the second best considering the SMAPE, afteronly ECMWF, and followed closely by SWAN. This was due to the fact that both ECMWF and SWANmodelled the contribution of waves with higher Hs better than SPM ’84 in the NW sector, while SPM’84modelled the directional distribution better.

Analyzing the correlation in each class of Hs between the observations and each model, Figure 12shows scatter plots of each hindcasting model af versus the observed af. Each subplot shows the valuesof the coefficient of determination, R2 calculated as:

R2 = 1− SSres

SStot(13)

where SSres is the sum of squares of residuals while SStot is the total sum of squares (proportional tothe variance of the data).

The best performance in terms of the correlation was shown by ECMWF (R2 = 0.856) and SWAN(R2 = 0.831); SPM ’84 was third (R2 = 0.618).

To facilitate the comparative assessment of the different hindcasting models, Figure 13 showsa Taylor diagram [54] representing the performance of each model. Taylor diagrams are used toquantify the degree of correspondence between the modelled and observed behavior in terms ofthree statistics: the Pearson correlation coefficient, related to the azimuthal angle (in blue), the RMSE(green), and the standard deviation (black). The Pearson correlation coefficient (gauging similarityin pattern between the simulated and observed af ) is related to the azimuthal angle; the centeredRMSE in the modelled af is proportional to the distance from the point on the x-axis identified as“reference”; and the standard deviation of the modelled af distribution is proportional to the radialdistance from the origin. Therefore, Figure 13 shows that all the models had a standard deviation(grey dotted contours) much larger than the observed data, which have a standard deviation of 3.03.The Pearson correlation coefficient was high for SWAN and ECMWF (>90%) compared to SPM ’84(80%), but SWAN and ECMWF also presented a much higher RMSE (>5%) and a larger standarddeviation (>7.5%) compared to the SPM ’84. Therefore, the Taylor diagram showed that the SPM ’84exhibited the best performance among the considered models.

Water 2018, 10, 985 15 of 19Water 2018, 10, x FOR PEER REVIEW 15 of 19

Figure 12. Scatter plots of each hindcasted model af versus the observed af. Figure 12. Scatter plots of each hindcasted model af versus the observed af.Water 2018, 10, x FOR PEER REVIEW 16 of 19

Figure 13. Taylor diagram of the performance of each of the considered models.

4. Discussion and Conclusions

Where the ADCP instrument was deployed, the observed wave climate had been obtained and compared with the wave climate determined by means of different models at the same location: wave propagation of the NOAA offshore wave dataset conducted by the SWAN numerical model, assuming wave conditions at the NOAA offshore grid point as boundary conditions; the NOAA and ECMWF wave dataset at the closest grid point; and the SPM ’84 [1] hindcasting method with the closest NOAA wind dataset used as input. The analysis of the wave characteristics has been expressed in terms of distributions of individual wave heights and directions.

The predictive capability of the SPM ’84 has been favorably verified against the observed and calculated wave climates. The estimated af RMSE showed that SPM ’84 resulted in a better agreement with the observed data compared to the other investigated models, and SPM ’84 exhibited the smallest af RMSE (3.55%), followed by SWAN (8.52%), ECMWF (9.36%), and NOAA N and S nodes (13.27% and 13.20%, respectively). Considering a symmetric statistical indicator, such as the SMAPE, SPM ’84 showed a comparable performance to ECMWF and SWAN. The reason for this was that ECMWF and SWAN simulated waves well in the NW sector with high Hs. The principal limitation of the latter two models was their limited representation of the wave directional distribution; mainly due to the assumed NOAA offshore directional distribution and to the limited bathymetrical grid, respectively.

Although SWAN, similarly to WW3 and WAM, used by NOAA and ECMWF, respectively, was a third-generation wave model, it showed better performance in determining the wave characteristics at Saadiyat with respect to NOAA and ECMWF models. This was due to the fact that SWAN contains some additional parameterizations primarily for shallow water [46], different numerical techniques, and different formulations for the wind input and the white-capping with respect to WW3. In addition, it used the higher resolution computational grid and bathymetry in the model implementation, as was shown in Table 3.

A Taylor diagram (Figure 13) of the overall performance of each of the considered wave hindcasting methods showed that the best agreement with the observed wave climate in the vicinity of Saadiyat beach at Abu Dhabi was obtained using the SPM ’84 hindcasting method for the shallow water condition. On the contrary, more sophisticated atmosphere–ocean numerical models, such as those used by NOAA and ECMWF, presented some limitation.

Figure 13. Taylor diagram of the performance of each of the considered models.

Water 2018, 10, 985 16 of 19

4. Discussion and Conclusions

Where the ADCP instrument was deployed, the observed wave climate had been obtained andcompared with the wave climate determined by means of different models at the same location:wave propagation of the NOAA offshore wave dataset conducted by the SWAN numerical model,assuming wave conditions at the NOAA offshore grid point as boundary conditions; the NOAA andECMWF wave dataset at the closest grid point; and the SPM ’84 [1] hindcasting method with theclosest NOAA wind dataset used as input. The analysis of the wave characteristics has been expressedin terms of distributions of individual wave heights and directions.

The predictive capability of the SPM ’84 has been favorably verified against the observed andcalculated wave climates. The estimated af RMSE showed that SPM ’84 resulted in a better agreementwith the observed data compared to the other investigated models, and SPM ’84 exhibited the smallestaf RMSE (3.55%), followed by SWAN (8.52%), ECMWF (9.36%), and NOAA N and S nodes (13.27%and 13.20%, respectively). Considering a symmetric statistical indicator, such as the SMAPE, SPM ’84showed a comparable performance to ECMWF and SWAN. The reason for this was that ECMWF andSWAN simulated waves well in the NW sector with high Hs. The principal limitation of the lattertwo models was their limited representation of the wave directional distribution; mainly due to theassumed NOAA offshore directional distribution and to the limited bathymetrical grid, respectively.

Although SWAN, similarly to WW3 and WAM, used by NOAA and ECMWF, respectively, was athird-generation wave model, it showed better performance in determining the wave characteristics atSaadiyat with respect to NOAA and ECMWF models. This was due to the fact that SWAN containssome additional parameterizations primarily for shallow water [46], different numerical techniques,and different formulations for the wind input and the white-capping with respect to WW3. In addition,it used the higher resolution computational grid and bathymetry in the model implementation, as wasshown in Table 3.

A Taylor diagram (Figure 13) of the overall performance of each of the considered wavehindcasting methods showed that the best agreement with the observed wave climate in the vicinityof Saadiyat beach at Abu Dhabi was obtained using the SPM ’84 hindcasting method for the shallowwater condition. On the contrary, more sophisticated atmosphere–ocean numerical models, such asthose used by NOAA and ECMWF, presented some limitation.

The SPM ’84 best performance could also be due to the fact that the SPM ’84 was based onexact equations (cfr. Equations (3)–(6)) and exact input terms, such as fetches, water depths, windcharacteristics, and therefore, not influenced by the resolution of the computational grid or thebathymetric information. The SPM ’84 could be improved, aiming at better modelling waves withhigh Hs by recalculating the numerical factors that appear in Equations (3)–(6), or calibrating themethod before the application by using a subset of the wave observations. In the case of Saadiyatbeach, it was not possible to perform this calibration for the time being due to the limited statistics ofwave observations collected so far.

The reliability in wave modelling from the application of the SPM ’84 can lead to a better planningof the ambitious coastal interventions that are foreseen in the Gulf area in the next future.

Author Contributions: G.R.T. and L.L. collected all the data, conceived and designed the application of theSPM ’84 method; L.L. analyzed the data, and implemented SWAN and the application of the SPM ’84 method;F.L., W.H., and F.D’A. contributed to the discussion regarding the results; G.R.T. and L.L. wrote the paper.

Funding: This work was funded by the United Arab Emirates University research grant, through the NationalWater Center, Grant # 31R115; “Impact of coastal (long-shore) currents on erosion/deposition and consequentwater/sediments quality variations along the coastal area of Abu Dhabi City” and by the Apulia Region (Italy),through the Regional Cluster Projects “Start”, Grant # 0POYPE3 and “Eco-Smart Breakwater”, Grant # S6LU5I7.

Acknowledgments: The authors thank the Abu Dhabi Municipality for providing in situ data relative to waveconditions at Saadiyat beachfront.

Conflicts of Interest: The authors declare no conflict of interest and the funding sponsors had no role in thedesign of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in thedecision to publish the results.

Water 2018, 10, 985 17 of 19

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